Want to Make More Baskets? Science Has the Answer


This effect is so pronounced that the study advises those seeking accuracy to throw as slowly as possible while still reaching their target.

The professors, Venkadesan and Lakshminarayanan Mahadevan of Harvard, did not line up dozens of undergraduates with baseballs and javelins for the study. Instead, their conclusions are based on mathematical modeling.

“What our work adds is a physics basis for why there is a speed/accuracy contrast,” Venkadesan said.

But they also compared their findings with data taken from athletes and found that the figures matched nicely.

For example, the study suggests that the optimal speed for a thrown dart is 5.1 to 5.5 meters per second. Typical dart throwers toss at an average speed of 5.8 to 6.7 meters per second, not far off.

Again, slowness pays off. Of the suggested speed, Venkadesan said, “That’s about as slow as you can throw while still sticking the dart in the board.” If the throw was any slower it “would completely miss the board, or it is going to enter at a very glancing blow.”

Humans tend to have discovered, without doing any math, the correct speeds to throw in sport after sport. “By trial and error, people learn what to do,” Venkadesan said. “We have the ability to learn. We learn over one lifetime: Babies start throwing and get feedback.”

One reason humans are so good at throwing may be that for tens of thousands of years they relied heavily on hunting for survival. “Hunting is a big part of the story,” Venkadesan said. “In the context of hunting, being fast and accurate is a challenging thing.”

Though we think of cave men hunting with spears, there is evidence that earlier hunting relied on throwing rocks. Getting the mechanics of throwing right could have been the difference between a protein-rich dinner and hunger.

And humans have unusually good throwing abilities. “Chimpanzees are slow and not accurate,” Venkadesan said. “They can barely throw as fast as a 10-year-old human.”

The researchers found one exception to the “slower is better” rule: cricket. When players are trying to hit the wicket — a small vertical target — to get a run out, “the best way is an underhand throw as fast as you can,” Venkadesan said. “It comes out of the math.”

The rule also might not be of much use in baseball and other sports in which someone is trying to hit the ball. Although slower pitches would be more accurate, they would also be easier to clobber into the bleachers — unless they curve or slide or knuckle, of course.

The professors offer some unorthodox basketball advice: Consider throwing free throws underhanded.

“The underarm throw is marginally better for an average N.B.A. player,” the paper said. The professors suggest that the reason more players have not tried the style is simply societal pressure — it looks kind of silly.

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